july 2007 richard blundell andrew shephard …uctp39a/blundell wpeg slides 10...2010/07/07 · and...

1

Tax-Credit Policies for Low Income Families:

Impact and OptimalityJuly 2007

Richard Blundelland

Andrew ShephardUniversity College London and

Institute for Fiscal Studies

WPEG 2007

• This research concerns the impact of tax and tax-credit reform on working decisions.

• It looks at the impact and the ‘optimal’ design• Two questions:

– How should we measure the impact of tax and tax-credits on work decisions?

– How should we assess the optimality of tax and tax-credit proposals?

• Focus on single mothers and the UK reforms

Tax-Credit Policies for Low Income Families

2

• Sequence of Tax Credit expansions– FC (family credit) before 2000, expanded early in

1990s– WFTC (working families tax credit) reform in 2000,

and subsequent expansions in 2002– influenced by the success of the EITC expansion in

the US– especially generous to families with young children

• WTC (working tax credit) and CTC (child tax credit) reform in 2004– extension of eligibility to individuals without

children

Tax Credit reforms in the UK

The WFTC Reform

00 10 20 30 40 50 60 70

Hours worked per week

Tra

nsfe

r

Family Credit WFTC

70%

55%

transfers per week for a min. wage lone parent

3

• Credit depends on earnings and number of children:– Phase-in: credit is flat percentage of earned

income or jump in at minimum hours threshold

– Flat range: receive maximum credit– Phase-out: credit is phased out at a flat rate

• Credit based on family earnings– Creating ‘interesting’ incentives among

couples

General form of Earned Income Tax Credits

EITC Schedule in US – Single Parent Families, 2004

Larger credit, covering higher earners for families with two or more children.

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$0 $5,000 $10,000 $15,000 $20,000 $25,000 $30,000 $35,000 $40,000Earnings

EIT

C C

redi

t

Two or more children One Child

Phase In Region

Flat Region

Phase-out Region

4

• Does the WTFC represent an optimal transfer for low income families?

• New insights from optimal tax theory show some negative marginal tax rates can be an optimal design

• Labour supply estimation suggest extensive margin is more responsive to incentives than intensivemargin

• This turns out to be a key observation for optimal tax design

Can a WFTC type design be ‘optimal’?

00

After Tax Income

Earnings

Negative Income Tax (NIT)

Tax Credit Policies for Low Income Families

break even pointguaranteed

income

‘top’ rate constrained by some political economy or taxable income elasticity argument

5

00

After Tax Income

Earnings

Earned Income Tax Credit (EITC)

Tax Credit Policies for Low Income Families

break even point

subsidy or‘phase-in’region

‘phase-out’region

In the research design reported here, the analysis of tax-credit policy is tackled in two steps:

• The first step is a positive analysis of how household work decisions respond. There are two empirical approaches - both prove useful:(a) A ‘quasi-experimental’ evaluation of the impact

of historic reforms(b) A ‘structural’ estimation of individual behaviour

based on a general discrete choice model• The second step is the normative analysis or optimal

policy analysis

The Analysis of Tax Credit Policies

6

• Two ‘new’ approaches• solve directly given the microeconometric estimates

of discrete choice behaviour and tax-benefit constraints

• take approximations in terms of underlying elasticities and welfare weights on different incomes – Diamond/Saez

• choose transfers and taxes ‘T’ to maximise welfare• extend the standard Mirrlees framework to allow for

responses at the extensive and intensive margin

A simple optimal design framework

Suppose U is the ‘utility’ of a single mother

A (simple) optimal tax framework

from working h hours with net income c, where X are observable characteristics of her and her child and ε represents unobserved characteristics.

Budget constraint:

( , ; )c w h T w h X≡ −

( , ; , )U c h X ε

Choose h from a set of discrete alternatives reflecting part-time work, full-time work etc.

7

Social welfare, for single parents of type X*( ( ( , ; ), ; , )) ( ) ( ; )i i i i i

i w

W u wh T w h X h X dF dG w Xε

ε ε= Γ −∑∫∫

( , ; ) ( ) ( ; ) ( )( ( ))i ii w

T w h X dF dG w X T X R Xε

ε = = −∑∫ ∫

The tax structure T(X) is chosen to maximise W, subject to:

A simple optimal tax/tax-credit framework

where Γ is the social welfare transformation.

• Suppose we distinguish between earnings groups– ‘no’ earners: group 0– ‘higher’ earners groups i = 1, 2,…

• Suppose the social welfare weight is higher for group 0, and monotonically decreasing

• Choose taxes (and transfers) T to maximise welfare

• Can derive expressions in terms of elasticities and social welfare weights across the income distribution

Simplified expressions - for intuition

8

Optimal design gives:

0 1g >

where

iζ is the labour supply elasticity

0

0

1i i

i i

T T gc c ζ− −

=−

iT− is the subsidy given to group i

ic is the net of tax income for that group is the social welfare weight for group iigand , with the weighted sum of g’s =1

Simplified expressions

00

After Tax Income

Earnings

An Optimal Schedule

region with g < 1

EITC ‘bubble’ region with g > 1

9

e.g. for two groups:

which leads to a standard NIT

1 0 0

1 0 1

1T T gc c ζ− −

=−

Simplified expressions

00

After Tax Income

Earnings

An Optimal Schedule

10

Suppose we now introduce an intensive and extensive margin

where

a ‘large’ extensive elasticity can ‘turn around’ the impact of social weights - implying a higher transfer to low wage workers than to those out of work – a tax-credit

,j jjg g kη= +

The intensive and extensive margin

1

1

1 [1 ]I

i ij

j ii i i

T T gc c ζ

−

=−

−= −

− ∑

iζ is the intensive elasticity

and jη is the extensive elasticity

00

After Tax Income

Earnings

A ‘Typical’ Optimal Schedule

‘NIT adapted’ EITC ‘bubble’

11

The US Earned Income Tax Credit

£0

£1,000

£2,000

£3,000

£4,000

£5,000

£6,000

£0 £5,000 £10,000 £15,000 £20,000 £25,000

Gross income (£/year)

EITC

• work eligibility– 16 or more hours per week

• family eligibility– children (in full time education or younger)

• income eligibility– if a family's net income is below a certain

threshold, adult credit plus age-dependent amounts for each child

– if income is above the threshold then the amount of credit is tapered away at 55% per extra pound of net income – previously 70%

The WFTC design: eligibility criteria

12

£0

£1,000

£2,000

£3,000

£4,000

£5,000

£6,000

£0 £5,000 £10,000 £15,000 £20,000 £25,000

Gross incom e (£/year)

EITC

WFTC

The UK and US tax credit systems compared

• A puzzle on the relative impact of WFTC and EITC

• Is this an ‘optimal’ design given efficiency and distributional considerations:

• Is an hours eligibility rule optimal?• At what hours point should it be set?• Is the overall structure of the WFTC optimal?

The WFTC design

13

• interaction with other benefits and taxes matter– differing size of the ‘treatment’ across eligibles

• coincident reforms to Income Support (IS)– different direction of these reforms to US

Unlike the US EITC the credit is based on net (rather than gross) family income

Interactions with other taxes and benefits

£0.00

£50.00

£100.00

£150.00

£200.00

£250.00

£300.00

0 4 8 12 16 20 24 28 32 36 40 44 48

hours of work

WFTCNet earningsOther income

WFTC interactions with other taxes and benefits in the UK

single parent on minimum wage

14

£0.00

£50.00

£100.00

£150.00

£200.00

£250.00

£300.00

0 5 10 15 20 25 30 35 40 45 50

hours of work

WFTCIncome SupportNet earningsOther income


£0.00

£50.00

£100.00

£150.00

£200.00

£250.00

£300.00

0 5 10 15 20 25 30 35 40 45 50

hours of work

Local tax rebateRent rebateWFTCIncome SupportNet earningsOther income


15

£0.00

£50.00

£100.00

£150.00

£200.00

£250.00

£300.00

0 5 10 15 20 25 30 35 40 45 50

hours of work

Local tax rebateRent rebateWFTCIncome SupportNet earningsOther income

fixed costs may be important

The interaction with other benefits

• Requires a reliable structural simulation model that captures decisions and the budget constraint accurately

• Two components:• budget constraint is approximated by number

of discrete points. • choose hours of work according to discrete

choice model with hours options:

Assessing the design

16

Fra

ctio

n

tothours16 30 40 50

.05

.1

.15

Weekly Hours WorkedLow Education Single Mothers (aged 18-45)

Lower hours limit

Fra

ctio

n

tothours16 30 40 50

.05

.1

.15

Weekly Hours WorkedLow Education Single Childless Women (aged 18-45)

17

• budget constraint that allows for tax/benefit interactions

• discrete decisions over hours worked

• heterogeneity – demographics, ethnicity,., unobs. het.

• fixed costs of work – obs. and unobs. het.

• stigma/hassle costs – take-up versus eligibility

• childcare costs

• do individuals behave this way?

Key features of a ‘realistic’ structural model

Specifying a structural labour supply model

( , ) ( , )h h hU h y u h y ε= +

• Where is a discrete hours choice specific errorhε

2 211 22 12 1 2( , )h h h h hU h y y h y h y hα α α β β ε≈ + + + + +

• Heterogeneity enters model through andα β

• For lone parents say, utility function defined over net income and hours:

• Approximate function by:

- observed and unobserved heterogeneity

18

{ } { }Pr[ ] exp ( , ) exp ( , )j kj j h k h

k

h h U h y U h y∈Θ

= = ∑

• lone parents choose hrs/wk point

• to maximise utility. With extreme value errors:{ }0,10,19, 26, 33, 40h ∈

• Model additionally allows for:• Unobserved work-related (fixed) costs, WRC• Childcare costs, CC• Programme participation (hassle or ‘stigma’) costs, P

Specifying a structural labour supply model

Take-up and WFTCVariation in take-up probability with entitlement to FC/WFTC

0.2

.4.6

.81

Pro

babi

lity

of ta

ke-u

p

0 5 0 100 1 50 2 00FC/W FTC enti tlem en t (£/we ek , 20 02 prices )

Lo ne paren ts Cou ples

FR S

19

Estimation

• Data from 1995-2003 (Family Resources Survey)– 1995-1999: pre-reform estimation data (ex-ante)– 2002-2003: ‘post-reform’ validation sample – Use complete sample for ex-ante analysis of 2004

and more recent reform proposals

Structural Model Elasticities

1.1295Participation elasticity0.08290.49200.16183000.23440.71370.17232200.39440.77090.14531400.50290.50290.124080

0.39660IntensiveExtensiveDensityEarnings

(a) Youngest Child Aged 11-18

20

Structural Model Elasticities

0.6352Participation elasticity0.08340.49840.06133000.10780.58650.07672200.15700.65340.09841400.26150.26150.169480

0.59420IntensiveExtensiveDensityEarnings

(c) Youngest Child Aged 0-4

• Check the robustness of the structural model by the ability to simulate the impact of the WFTC reform

Structural Evaluation Simulation Results: WFTC Expansion

Notes: Simulated on FRS data; Standard errors in italics.

All: 5.12 without change in take-up – key impact effect

All y-child y-child y-child y-child0 to 2 3 to 4 5 to 10 11 to 18

Change in employment rate: 5.95 3.09 7.56 7.54 4.960.74 0.59 0.91 0.85 0.68

Average change in hours: 1.79 0.71 2.09 2.35 1.650.2 0.14 0.23 0.34 0.2

21

Adult and Child Elements of the WFTC

Note: All monetary amounts are expressed in April 2003 prices.

Adult Child Awards by Agechild child child

0 to 10 11 to 15 16 to 18Mar-99 £58.80 £16.40 £22.60 £28.00Oct-99 £56.60 £21.50 £22.60 £28.00Mar-00 £56.60 £22.60 £22.60 £28.00Jun-01 £61.90 £27.30 £27.30 £28.00Jun-02 £64.40 £27.30 £27.30 £28.00

Increase 19.70% 66.40% 20.50% 0.00%

Impact of WFTC reform on lone parent, 2 children

£100

£150

£200

£250

£300

0 4 8 12 16 20 24 28 32 36 40 44 48

Hours/week

Wee

kly

net i

ncom

e 1999 2000 2002

• Notes: Two children under 5. Assumes hourly wage of £4.10, no housing costs or council tax liability and no childcare costs.

22

child child child0 to 10 11 to 15 16 to 18

Mar-99 £21.90 £28.00 £33.50Oct-99 £27.00 £28.00 £33.50Mar-00 £28.40 £28.40 £33.80Mar-01 £33.00 £33.00 £33.80Oct-01 £34.50 £34.50 £35.40Mar-02 £34.50 £34.50 £35.40

Increase 57.50% 23.30% 5.70%

Child Rates of Income Support

Note: All monetary amounts are expressed in April 2003 prices.

Impact of WFTC & increases in welfare benefit on lone parent, 2 children

£100

£150

£200

£250

£300

0 4 8 12 16 20 24 28 32 36 40 44 48

Hours/week

Wee

kly

net i

ncom

e 1999 2000 2002

• Notes: Two children under 5. Assumes hourly wage of £4.10, no housing costs or council tax liability and no childcare costs.

23

Structural Evaluation Simulation Results: All Reforms

Notes: Simulated on FRS data; Standard errors in italics.

All y-child y-child y-child y-child0 to 2 3 to 4 5 to 10 11 to 18

Change in employment rate: 3.68 0.65 4.53 4.83 4.030.84 0.6 0.99 0.94 0.71

Average change in hours: 1.02 0.01 1.15 1.41 1.240.23 0.21 0.28 0.28 0.22

• Compare structural model simulations based on estimated parameters to quasi-experimental ex-post evaluation

• The idea is to simulate the quasi-experimental estimate (moment)

• comparing work decisions of eligible versus those who are not eligible before and after the reform

• identify average employment impact on eligibles by assuming a structure on unobservables– separability– common trends across groups– invariance in group heterogeneity over time

• conditional on a set of (matching) covariates X

Robustness of the structural model:

24

Employment rates of single women in the UK

30

40

50

60

70

80

1997

Q1

1998

Q1

1999

Q1

2000

Q1

2001

Q1

2002

Q1

2003

Q1

2004

Q1

Em

ploy

men

t rat

e (%

)Lone parentsSingle Women without children

Difference-in-Differences: Lone Mothers Employment

233,2080.333.81Labour Force Survey

74,9590.813.57Family Resources Survey

Sample SizeStandard Error

Marginal Effect

Single Women

Data: Spring 1996 – Spring 2003.

Drop: Summer 1999 – Spring 2000 inclusive; individuals aged over 45.

Outcome: employment. Average impact x 100, employment percentage.

Matching Covariates: age, education, region, ethnicity,..

25

• The simulated diff-in-diff parameter from the structural evaluation model is precise and does not differ significantly from the diff-in-diff estimate

• Compare simulated diff-in-diff moment with diff-in-diff – .29 (.73), chi-square p-value .57

• Consider additional moments– education: low education: 0.33 (.41) – youngest child interaction

• Youngest child aged < 5: .59 (. 51)• Youngest child aged 5-10: .31 (.35)

Evaluation of the ex-ante model

What of the ‘optimal’ design?

• Given the structural discrete choice estimates and the implied elasticities at extensive and intensive margin, we can pose the question:

– what is the optimal tax and transfer schedule?

– is the WFTC+ ‘optimal’ for reasonable social welfare weights?

{ }1( | ) (exp ) 1U U θθθ

Γ = −

• When θ is negative, the function favours the equality of utilities; We solve the schedule for a series of values – central estimates us -0.2

26

Should there be an hours eligibility condition or ‘bonus’?

• Is it optimal to have a ‘minimum hours’eligibility?

• If we can have a 16 hours condition, what should it look like?

• Is 16 the optimal choice?

An Optimal Schedule, Youngest Child Aged 0-4

100.00

150.00

200.00

250.00

300.00

0 50 100 150 200 250 300

No hours ruleWeekly earningsMarch 2002 prices

27


100.00

150.00

200.00

250.00

300.00

0 50 100 150 200 250 300

No hours rule 16 hours rule

Weekly earningsMarch 2002 prices£6 per hour


100.00

150.00

200.00

250.00

300.00

350.00

0 50 100 150 200 250 300

No hours rule 16 hours ruleWeekly earningsMarch 2002 prices

28


100.00

150.00

200.00

250.00

300.00

350.00

0 50 100 150 200 250 300

No hours rule 16 hours rule

Weekly earningsMarch 2002 prices


100.00

150.00

200.00

250.00

300.00

350.00

0 50 100 150 200 250 300

No hours rule 16 hours rule Optimal hours rule

29


100.00

150.00

200.00

250.00

300.00

350.00

0 50 100 150 200 250 300


An Optimal Schedule, Impact on Hours worked, Youngest Child Aged 5-10

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 19 26 33 40

no hours 16 hours opt hours

30

Social Welfare Weights

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2 3 4 5

0.2 0 -0.2

The impact of welfare weights: Youngest Child Aged 5-10

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0 50 100 150 200 250 300

theta=-0.2 theta=0.0 theta=0.2

31

Implications?• Resolved the US-EITC, UK-WFTC puzzle• WFTC/IS type schedule looks optimal overallBut• Age of children matter

– Only reduce current marginal tax rates on participation for parents with children of school age

• Hours rules can be optimal• No hours conditioning for mothers with youngest

child less than 5, higher hours condition for mothers with older child.

• Administration and integration

• What of work experience and wages?• Indeed what is the long-term program impact on

gross wages?• Couples decision making?

– UK has moved to individual income taxation but in-work tax credits are family income based

– targeting in collective labour supply models• What impact on fertility and family formation?

Extensions: ….

32

Reform impacts on budget constraints for mother in couple

Notes: Two children under 5. Assumes hourly wage of £4.10, no housing costs or council tax liability and no childcare costs.The first earner in the couple is assumed to earn £300 per week in 2002 prices.

260

280

300

320

340

360

380

400

420

440

460

0 5 10 15 20 25 30 35 40 45 50

Hours worked

Net

inco

me

(£ p

.w.,

2002

pric

es)

1999 2000

2002

• Work experience and earnings?– Card and Hyslop (2004)– SSP Canadian single parents

• ERA results for the UK?

Experience and Wages

33

.1.1

5.2

.25

.3E

mpl

oym

ent r

ate

0 10 20 30 40 50 60Months after random assignment

control experimental

SSP experiment: dynamic effects on employment rates?

66.

57

7.5

88.

5H

ourly

real

wag

es

0 10 20 30 40 50 60Months after random assignment

control experimental

SSP experiment: dynamic effects on wages and productivity?

34

• The Integrated Family Supplement? – The ‘IFS’

• Mirrlees Review…– www.ifs.org.uk/mirrleesreview

Extensions: More to do….

Some References:Beaudry, P., and C. Blackorby (2000), “Taxes and Employment Subsidies in Optimal Redistribution Programs”, Discussion Paper 22, UBC, October.

Besley, T. and S. Coate (1992), “Workfare versus Welfare: Incentive Arguments for Work Requirement in Poverty Alleviation Programs”, American Economic Review, 82(1), 249-261.

Blundell, R. (2006), “Earned income tax policies: Impact and Optimality”, The 2005 Adam Smith Lecture to the Society of Labor Economics, Labour Economics, 13, 423-443.

Blundell, R.W., Duncan, A. and Meghir, C. (1998), "Estimating Labour Supply Responses using Tax Policy Reforms", Econometrica, 66, 827-861.

Blundell, R, Duncan, A, McCrae, J and Meghir, C. (2000), "The Labour Market Impact of the Working Families' Tax Credit", Fiscal Studies, 21(1).

Blundell, R. and Hoynes, H. (2004), "In-Work Benefit Reform and the Labour Market", in Richard Blundell, David Card and Richard .B. Freeman (eds) Seeking a Premier League Economy. Chicago: University of Chicago Press.

Blundell, R. and MaCurdy (1999), "Labour Supply: A Review of Alternative Approaches", in Ashenfelter and Card (eds), Handbook of Labour Economics, Elsevier North-Holland

35

Brewer, M. (2003), “The New Tax Credits”, IFS Briefing Note No. 25, www.ifs.org.uk

Brewer, M. A. Duncan, A. Shephard, M-J Suárez, (2006), “Did the Working Families Tax Credit Work?”, Labour Economics, 13(6), 699-720.

Card, David and Philip K. Robins (1998), "Do Financial Incentives Encourage Welfare Recipients To Work?", Research in Labor Economics, 17, pp 1-56.

Diamond, P. (1980): "Income Taxation with Fixed Hours of Work," Journal of Public Economics, 13, 101-110.

Eissa, Nada and Jeffrey Liebman (1996), "Labor Supply Response to the Earned Income Tax Credit", Quarterly Journal of Economics, CXI, 605-637.

Gregg, P. and S. Harkness (2003), “Welfare Reform and Lone Parents in the UK”, CMPO Working Paper Series, 03/072.

Immervoll, H. Kleven, H. Kreiner, C, and Saez, E. (2004), `Welfare Reform in European Countries: A Micro-Simulation Analysis’ CEPR DP 4324, forthcoming Economic Journal.

Keane, M.P. (1995) `A New Idea for Welfare Reform', Quarterly Review, Federal Reserve Bank of Minneapolis, Spring, pp 2 - 28.

Keane, M.P. and Moffitt, R. (1998), "A Structural Model of Multiple Welfare Program Participation and Labor Supply", International Economic Review, 39(3), 553-589.

Laroque, G. (2005), “Income Maintenance and Labour Force Participation”, Econometrica, 73(2), 341-376.

Liebman, J. (2002), ‘The Optimal Design of the Earned Income Tax Credit’, in Bruce Meyer and Douglas Holtz-Eakin (eds.), Making Work Pay: The Earned Income Tax Credit and Its Impact on American Families, New-York: Russell Sage Foundation.

Mirrlees, J.A. (1971), “The Theory of Optimal Income Taxation”, Review of Economic Studies, 38, 175-208.

Moffitt, R. (1983), "An Economic Model of Welfare Stigma", American Economic Review, 73(5), 1023-1035.

Moffitt, R. (2005), "Welfare Work Requirements with Paternalistic Government Preferences, mimeo, Johns Hopkins University, February.

Phelps, E.S. (1994), “Raising the Employment and Pay for the Working Poor”, American Economic Review, 84 (2), 54-58.

Saez, E. (2002): "Optimal Income Transfer Programs: Intensive versus Extensive Labor Supply Responses," Quarterly Journal of Economics, 117, 1039-1073.

Seade, J.K. (1977), “On the Shape of Optimal Income Tax Schedules” Journal of Public Economics, 7, 203-236.

36

Tax-Credit Policies for Low Income Families:

Impact and Optimality

Extra Slides

1996 1997 1998 1999 2000 2001 2002No Work 0.753 0.762 0.769 0.770 0.774 0.767 0.775child

Age 26.789 26.906 26.799 26.957 27.104 27.317 27.450Non-white 0.073 0.077 0.080 0.084 0.091 0.098 0.102Left education before 16 0.078 0.072 0.062 0.057 0.052 0.047 0.043Left education at 16 or 17 0.394 0.381 0.375 0.375 0.363 0.353 0.356London and South-East 0.341 0.350 0.349 0.347 0.354 0.360 0.352Rented accommodation 0.343 0.353 0.358 0.340 0.339 0.350 0.346

Observations 26243 24463 24410 23987 22558 23517 22846

Child Work 0.417 0.425 0.444 0.464 0.477 0.487 0.496

Age 32.330 32.580 32.655 32.863 33.181 33.280 33.288Non-white 0.100 0.099 0.091 0.098 0.106 0.112 0.111Left education before 16 0.209 0.196 0.189 0.169 0.154 0.161 0.155Left education at 16 or 17 0.632 0.627 0.633 0.635 0.646 0.641 0.637London and South-East 0.285 0.285 0.285 0.293 0.294 0.303 0.301Rented accommodation 0.686 0.704 0.708 0.696 0.697 0.694 0.676Number of kids 1.783 1.785 1.791 1.784 1.778 1.776 1.794Age of youngest child 6.187 6.249 6.272 6.414 6.592 6.612 6.676Observations 14613 14172 14550 14343 13572 14097 13996

Table A1: Sample Descriptives for Single Women

37

Tax

Transfers

P: take-up

the tax-credit payment function depends on:

hours (through the hours condition of entitlement)

other income I

demographic characteristics X

Net Income schedule :

or

0 1( , ) ( , , ) ( , , )hP hy wh I t wh I C w h I P w h I= + − − +Ψ + Ψ

1( , , )hP hPy y P w h I= + Ψ

1( , , )w h IΨ

Utility ‘cost’ of receiving in-work support

Take-up

X u

UPhj ,yhj1 −C,P 1 Uhj ,yhj

−C.

claim 1 in FC/WFTC at hours hj if:

Uhj,yhj 1 − C −Uhj,y hj

− C

where C is the fixed cost of work. The utility cost among those who are eligible for WFTC at hours hj and choose to claim WFTC must not exceed the utility gain from receipt of WFTC transfer income relative to non-receipt:

u U U Uhj ,yhj1 −C −Uhj ,yhj

−C − Xwhere

38

and is ‘cost’ of receiving in-work support.

Preferences and Take-Up

UPh,yhP, P;C 11yh P 1 −C2 22h2 12

yh P 1 −C h 1

yh P 1 −C 2h hP − P Eh

Uh,yh P 1 −C − P Eh ,

The introduction of these additional terms is important in evaluation of a reform which increases generosity

X u

Eh 11 0where is an indicator of eligibility at hours h,

Preferences:

C represents the ‘fixed cost’ of work

Stochastic specification

1 X11x uy

2 X22x uh

11 X1111x

22 X2222x

12 X1212x

WRC1 Xf1f1 uf

WRC2 Xf2f2

Fixed costs of work

Stochastic Preferences

39

Childcare Costs

h cc Gh|Xcc

Ch;Xf,Xcc,pc,uf WRC1 Ih1 WRC2 Ih2 pc hcc

Xf1f1 uf Ih1 Xf2f2 Ih2 pc Gh|Xcc

At price pc for an hour of childcare per child

To estimate the childcare price per child pc, we compute the empirical distribution of hourly child-care costs for various groups of working mothers defined by their family status and number and age of children Xcc.

Prh h j , P p|X, u

where u u w , u y , u h , u cc , u f

expUhj,yhj

phj,Pp

∑k1

JmaxexpUhk ,y hk

,P0,EhkexpUhk ,yhk

hk,P1

Choice probabilities:

40

Likelihood specification

where

logL ∑i log u−u

uUj Prh hj,P 1|X,u1hhj,Ehj1,P1fudu


uj Prh hj,P 0|X,u1hhj,Ehj0fudu

fu−udu−u

P r( , | , )jh h P p X u= =

These preferences, fixed costs, childcare costs and stigma cost expressions provide the choice probabilities:

From which we construct the sample log likelihood:

( , , , , )u w y h f ccu u u u u uη− =

Likelihood specification

u−u uw,uy,uh,uf ,ucc

where

logL ∑i log u−u



uj Prh hj,P 0|X,u1hhj,Ehj0fudu

fu−udu−u

41

Structural Evaluation Model: Parameter Estimates

42

Award increased by 70% of childcare expenses up to £135 (£200) for 1 (more than 1) child under 15



Childcare expenses up to £60 (£100) for 1 (more than 1) child under 12 disregarded when calc income

Childcare

55% of earnings after income tax and NI




Taper94.591.459080.65Threshold11.6511.2511.0511.0530 hour 27.226.3525.9525.95over 1626.4525.620.920.911 to 1626.4525.619.8515.15under 11

Child Credit62.553.1552.349.8Basic Credit

(WFTC)(WFTC)(WFTC)(FC)

Jun-02Jun-00Oct-99Apr-99

43

Changes in marginal tax rates: all working parentsMarginal rates at the bottom remain high

0

1,000,000

2,000,000

3,000,000

4,000,000

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8,000,000

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100%

More than

90%

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70%

More than

60%

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50%

More than

40%

More than

30%

More than

20%

More than

10%

More than

0% Any

Wor

king

par

ents April 97

April 04

An Optimal Schedule, no hours condition

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yk510 yk04 yk1118

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The Structure of the Constraint, top-rate 50%

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july 2007 richard blundell andrew shephard …uctp39a/blundell wpeg slides 10...2010/07/07 · and...

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